Finite Group Databasebeta

← Group #116237

Character table — Group #116237

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222222244444444444444444444448888888822444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111
χ91-111-1-11-1-1-111-1-111111-1-111-1-1-1ii−i−iii−i−iiiii−i−i−i−i1-1i−i1-1i−i11-1-111-1-1ii−i−i
χ101-111-1-11-1-1-111-1-111111-1-111-1-1-1ii−i−iii−i−iiiii−i−i−i−i-11−ii-11−ii-1-11111-1-1−i−iii
χ111-111-1-11-1-1-111-1-111111-1-111-1-1-1ii−i−iii−i−i−i−i−i−iiiii1-1−ii1-1−ii-1-111-1-111ii−i−i
χ121-111-1-11-1-1-111-1-111111-1-111-1-1-1ii−i−iii−i−i−i−i−i−iiiii-11i−i-11i−i11-1-1-1-111−i−iii
χ131-111-1-11-1-1-111-1-111111-1-111-1-1-1−i−iii−i−iiiiiii−i−i−i−i1-1i−i1-1i−i-1-111-1-111−i−iii
χ141-111-1-11-1-1-111-1-111111-1-111-1-1-1−i−iii−i−iiiiiii−i−i−i−i-11−ii-11−ii11-1-1-1-111ii−i−i
χ151-111-1-11-1-1-111-1-111111-1-111-1-1-1−i−iii−i−iii−i−i−i−iiiii1-1−ii1-1−ii11-1-111-1-1−i−iii
χ161-111-1-11-1-1-111-1-111111-1-111-1-1-1−i−iii−i−iii−i−i−i−iiiii-11i−i-11i−i-1-11111-1-1ii−i−i
χ1722222222222222222-2-22-2-2-2-2-2-20000000000000000000000002-22-200000000
χ1822222222222222222-2-22-2-2-2-2-2-2000000000000000000000000-22-2200000000
χ19222222222222-2-2-2-2-222-22-2-2-22-22222-2-2-2-20000000000000000000000000000
χ20222222222222-2-2-2-2-222-22-2-2-22-2-2-2-2-222220000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2222-220000000000000000002200-2-2000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2222-22000000000000000000-2-20022000000000000
χ2322222222-2-2-2-22222-22-2-222-2-2-220000000022-2-222-2-200000000000000000000
χ2422222222-2-2-2-22222-22-2-222-2-2-2200000000-2-222-2-22200000000000000000000
χ2522222222-2-2-2-22222-2-22-2-2-2222-2000000000000000000000000000000002-22-2
χ2622222222-2-2-2-22222-2-22-2-2-2222-200000000000000000000000000000000-22-22
χ2722222222-2-2-2-2-2-2-2-222-222-222-2-200000000000000000000000000002i−2i2i−2i0000
χ2822222222-2-2-2-2-2-2-2-222-222-222-2-20000000000000000000000000000−2i2i−2i2i0000
χ2922222222-2-2-2-2-2-2-2-22-222-22-2-22200000000000000002200-2-200000000000000
χ3022222222-2-2-2-2-2-2-2-22-222-22-2-2220000000000000000-2-2002200000000000000
χ312-222-2-22-222-2-222-2-222-2-2-2-22-22200000000000000000000000000002i−2i−2i2i0000
χ322-222-2-22-222-2-222-2-222-2-2-2-22-2220000000000000000000000000000−2i2i2i−2i0000
χ332-222-2-22-222-2-222-2-22-22-222-22-2-200000000000000002-200-2200000000000000
χ342-222-2-22-222-2-222-2-22-22-222-22-2-20000000000000000-22002-200000000000000
χ352-222-2-22-222-2-2-2-222-22-22-22-222-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ362-222-2-22-222-2-2-2-222-22-22-22-222-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ372-222-2-22-222-2-2-2-222-2-2222-22-2-22000000000000000000000000000000002i−2i−2i2i
χ382-222-2-22-222-2-2-2-222-2-2222-22-2-2200000000000000000000000000000000−2i2i2i−2i
χ392-222-2-22-2-2-22222-2-2-2222-2-2-22-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ402-222-2-22-2-2-22222-2-2-2222-2-2-22-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ412-222-2-22-2-2-22222-2-2-2-2-22222-22-20000000000000000002i−2i00−2i2i000000000000
χ422-222-2-22-2-2-22222-2-2-2-2-22222-22-2000000000000000000−2i2i002i−2i000000000000
χ432-222-2-22-2-2-222-2-2222-2-2-22-2-22220000000000000000000000002-2-2200000000
χ442-222-2-22-2-2-222-2-2222-2-2-22-2-2222000000000000000000000000-222-200000000
χ45444-4-4-4-4400004i−4i4i−4i00000000002i−2i2i−2i2-22-20000000000000000000000000000
χ46444-4-4-4-4400004i−4i4i−4i0000000000−2i2i−2i2i-22-220000000000000000000000000000
χ47444-4-4-4-440000−4i4i−4i4i00000000002i−2i2i−2i-22-220000000000000000000000000000
χ48444-4-4-4-440000−4i4i−4i4i0000000000−2i2i−2i2i2-22-20000000000000000000000000000
χ4944-4-44-44-44-44-400000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ5044-4-44-44-44-44-40000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ5144-4-44-44-4-44-4400000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ5244-4-44-44-4-44-440000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ534-44-444-4-400004i−4i−4i4i00000000002-2-222i−2i−2i2i0000000000000000000000000000
χ544-44-444-4-400004i−4i−4i4i0000000000-222-2−2i2i2i−2i0000000000000000000000000000
χ554-44-444-4-40000−4i4i4i−4i00000000002-2-22−2i2i2i−2i0000000000000000000000000000
χ564-44-444-4-40000−4i4i4i−4i0000000000-222-22i−2i−2i2i0000000000000000000000000000
χ574-4-4-4-44444-4-4400000000000000000000002-2-22-222-200000000000000000000
χ584-4-4-4-44444-4-440000000000000000000000-222-22-2-2200000000000000000000
χ594-4-4-4-4444-444-400000000000000000000002-22-2-22-2200000000000000000000
χ604-4-4-4-4444-444-40000000000000000000000-22-222-22-200000000000000000000
χ6188-88-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8-888-8-88000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).